Non-contact inductive transmission of electrical power to rail-guided transfer units equipped with electric consumers has been known for a long time. For example, DE 44 46 779 describes an arrangement for non-contact inductive power transmission to electrically powered transfer units that are moved on a closed track. In this arrangement, a feeder fed by a higher-frequency AC power supply is kept at a spacing from the slide rail and encompassed by the respective current collector that is mounted to the respective transfer unit and connected to the drive motor and the control circuit. The current collector consists of a U-shaped ferrite core with a winding around its limbs. Transmission of electrical power from the primary feeder to the secondary windings is based on the transformer principle, and the various consumers on the transfer unit are supplied a voltage level in accordance with their power needs. As the control circuit of the transfer unit, however, requires a considerably lower voltage (24V) than the power circuit, an enormous switching effort is required to supply the 24V DC from the 560V DC voltage provided by the current collector. A similar effort is required for the return conductor of the primary power supply that in DE 44 46 779 is formed by the sidewalls of a casing that almost completely encompasses the current collector.